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2008 Moment estimates for Lévy Processes
Harald Luschgy, Gilles Pagès
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Electron. Commun. Probab. 13: 422-434 (2008). DOI: 10.1214/ECP.v13-1397


For real Lévy processes $(X_t)_{t \geq 0}$ having no Brownian component with Blumenthal-Getoor index $\beta$, the estimate $E \sup_{s \leq t} |X_s - a_p s|^p \leq C_p t$ for every $t \in [0,1]$ and suitable $a_p \in R$ has been established by Millar for $\beta < p \leq 2$ provided $X_1 \in L^p$. We derive extensions of these estimates to the cases $p < 2$ and $p \leq\beta$.


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Harald Luschgy. Gilles Pagès. "Moment estimates for Lévy Processes." Electron. Commun. Probab. 13 422 - 434, 2008.


Accepted: 5 August 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60098
MathSciNet: MR2430710
Digital Object Identifier: 10.1214/ECP.v13-1397

Primary: 60G51
Secondary: 60G18

Keywords: alpha-stable process , Lévy measure , Lévy process increment , Meixner process , Normal Inverse Gaussian process , tempered stable process

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